Exam 9: Introduction to Estimation

A(n)____________________ estimator of a population parameter is an estimator whose expected value is equal to that parameter.

An interval estimate is an estimate of the range for a sample statistic.

If we have some idea about the value of sample proportion , we use that value in determining the sample size needed to estimate the population proportion p.

Physicians A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. {Physicians Narrative} Can we conclude at the 1% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24?

The sample ____________________ is relatively more efficient than the sample ____________________ when estimating the population mean.

A point estimate consists of a single sample statistic that is used to estimate the true population parameter.

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors' results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:

The version of the sample variance where you divide by ____________________ gives you an unbiased estimator of the population variance.

Draw a sampling distribution of a biased estimator for m .

Which of the following would be an appropriate alternative hypothesis?

A random sample of 10 university students was surveyed to help estimate the average amount of time students spent per week on their computers. The student hours spent using a personal computer over a randomly selected week were 13, 14, 5, 6, 8, 10, 7, 12, 15, 3. a. Find an unbiased estimator of the average time per week for all university students. b. Find an unbiased estimator of the variance. c. Find a consistent estimator of the average time per week for all university students.

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows larger as the sample size grows larger.

Which of the following statements is correct?

As a manufacturer of guitars, a major corporation wants to estimate the proportion of guitar players who are right-handed. How many golfers must be surveyed if they want to be within 0.02, with a 95% confidence? found from a previous study, which suggests that 75% of guitar players are right-handed.

Socialist Party Voters A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that. In a test of hypothesis, H ₀: p = 0.05 vs. H ₁: p {Socialist Voters Narrative} Test the hypotheses at the 5% significance level.

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

If the bound on the error of estimation decreases, the sample size ____________________.

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient .

Draw the sampling distribution of two unbiased estimators for m , one of which is relatively efficient.

Draw a sampling distribution of an unbiased estimator for m .